VarEff estimates the effective sizes from actual to ancestral time with a coalescent approach. It works on steps of constant size to resolve the probabilities by an approximation of maximum likelihood from a Bayesian posterior distribution.
Migrate estimates effective population sizes and past migration rates between n population assuming a migration matrix model with asymmetric migration rates and different subpopulation sizes. Migrate uses maximum likelihood or Bayesian inference to jointly estimate all parameters.
It can use the following data types:
Sequence data using Felsenstein’s 84 model with or without site rate variation,
Single nucleotide polymorphism data (sequence-like data input, HAPMAP-like data input)
Microsatellite data using a stepwise mutation model or a brownian motion mutation model (using the repeatlength input format or the fragment-length input format),
Electrophoretic data using an ‘infinite’ allele model.